Demonstration of the Factory classes for reliability problems

In this example, we show how to use various classes which provide an easy way to create an algorithm to estimate a problem from a ReliabilityBenchmarkProblem. This methods do not set the parameters of the algorithm and do not run it, so that we can set specific settings for a given problem.

import openturns as ot
import otbenchmark as otb

We consider the RP8 problem.

problem = otb.ReliabilityProblem8()

Create a Monte-Carlo algorithm

The buildMonteCarlo method creates a ProbabilitySimulationAlgorithm based on MonteCarlo sampling. Before running the algorithm, we set the number of outer iterations based on the setMaximumOuterSampling method. This shows the main utility of the Factory classes.

factory = otb.ProbabilitySimulationAlgorithmFactory()
algo = factory.buildMonteCarlo(problem)
algo.setMaximumOuterSampling(100000)
algo.run()
result = algo.getResult()
result.getProbabilityEstimate()

0.0007399999999999966

Create a FORM algorithm

We use the FORM class applied to the problem.

nearestPointAlgorithm = ot.AbdoRackwitz()
algo = otb.FORM(problem, nearestPointAlgorithm)

The FORM object of the otbenchmark module implements a openturns.FORM object. Hence, it has a run method. If specific setting is required, we can do it now, prior to the call to the run method.

algo.run()

result = algo.getResult()
result.getEventProbability()

0.0006598990293278664

We can compare the previous estimate with the exact probability.

problem.getProbability()

0.0007897927545597477

Create a SORM algorithm

The SORM class creates a SORM object.

nearestPointAlgorithm = ot.AbdoRackwitz()
algo = otb.SORM(problem, nearestPointAlgorithm)

algo.run()

result = algo.getResult()
result.getEventProbabilityBreitung()

0.000783711312874782

Create a FORM-IS algorithm

The buildFORMIS method of the ProbabilitySimulationAlgorithmFactory class creates a ProbabilitySimulationAlgorithm object, based on the Importance Sampling method using the FORM design point with gaussian importance distribution.

factory = otb.ProbabilitySimulationAlgorithmFactory()
nearestPointAlgorithm = ot.AbdoRackwitz()
algo = factory.buildFORMIS(problem, nearestPointAlgorithm)
algo.run()
result = algo.getResult()
result.getProbabilityEstimate()

0.0008619170758804403

Create a SubsetSampling algorithm

algo = otb.SubsetSampling(problem)
algo.run()
result = algo.getResult()
result.getProbabilityEstimate()

0.0007137999999999998

Create a LHS algorithm

algo = otb.LHS(problem)
algo.run()
result = algo.getResult()
result.getProbabilityEstimate()

0.0009999999999999987